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Tasya [4]
3 years ago
8

If shown, AB and CD are straight lines. Find x in each case.

Mathematics
1 answer:
nlexa [21]3 years ago
4 0

Answer:

x = 60

Step-by-step explanation:

Vertical opposite angles are formed when two straight lines intersect each other.

Given that AD and CD are two straight lines intersecting at O, the two vertical opposite formed are, ∠AOD and ∠COB. Therefore:

∠AOD = ∠COB (Vertical opposite angles are congruent)

∠AOE = 90° (right angle)

∠DOE = x

∠COF = 30°

∠BOF = 2x

m∠AOE + m∠DOE = m∠AOD (angle addition postulate)

90 + x = ∠AOD (Substitution)

m∠COF + m∠BOF = m∠COB (Angle addition postulate)

30 + 2x = ∠COB

m∠AOD = m∠COB (vertical opposite angles)

90 + x = 30 + 2x (Substitution)

Collect like terms

90 - 30 = 2x - x

60 = x

x = 60

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